ceiling(harvest*sides) mostly returns a value between
1 and sides, with an extremely low probability of zero.
max(1,ceiling(harvest*sides)) the min doesn't do anything.
removes even that small probability. sides=t_tot=2*i_max+1,
the result is between 1 and 2*_max+1.
Later you subtract i_max, so between 1-imax and imax+1.
It seems you don't have bounds checking on, and you don't
notice the counts in k(i_max+1)
Either use floor() or int(), or subtract one.
As far as the original question, I believe it is
one fourth, not one eighth.
If you have two (approximately) symmetric distributions
uniform over, for example, the range (-1/2,1/2), that is,
the PDF is rect(x)
http://en.wikipedia.org/wiki/Rectangular_function
(Note that the result doesn't depend on rect(1/2) or rect(-1/2).)
The PDF of the difference is tri(x)
(the convolution of rect with itself)
http://en.wikipedia.org/wiki/Triangular_function
which has one fourth of its area outside (-1/2,1/2).
-- glen
